A multivariate quadrature based moment method for supersonic combustion modeling

Abstract

The joint probability density function (PDF) of thermochemical variables can be used for accurately computing the combustion source term. Quadrature based methods provide a computationally efficient and robust approach for estimating the PDF. The direct quadrature method of moments (DQMOM) is well suited for multivariate problems like combustion. Numerical implementation of DQMOM however leads to errors in estimating the PDF. In this work, a new quadrature based approach called semi-discrete quadrature method of moments (SeQMOM) that overcomes this problem is developed. A decoupling procedure allows extension of this method to multivariate problems. SeQMOM is then used for studying an experimental Mach 2.2 supersonic cavity based combustor.

Design of Dual-Mode Engine Flowpaths for Hypersonic Vehicles Using Reduced-Order Models

“…Equation 11 defines the Crocco number w, w (x) is the Crocco number between station 2 and station 3, b is an experimentally determined constant and p(x) is the static pressure in the isolator between p 2 and p 3 . The estimated length of the PCST, l, is determined by using Ikui's experimental correlation, l = 1 c ln(w 2 /w 3 ), where c is also experimentally determined.…”

“…In order to obtain a starting point for the design trade study, we begin with some designs that are available in the open literature. 2,11 These are laboratory scale combustors which are used for tests of combustion processes such as flame holding and combustion efficiency. It is important to note that these combustors are not necessarily designed to generate thrust, but they do provide a reasonable starting point for combustor design because they are combustors known to operate successfully.…”

“…Furthermore, the configurations used in the experiments cited were not able to be modeled without some modifications that allowed them to fit into the design structure that MASIV uses. Figure 6 shows the geometry of the combustor used by Donde et al, 11 which originates with Dr. James Donohue at United Technologies Research Corporation (UTRC). A data set for this combustor is not yet available.…”

Sensitivity analysis for Eulerian PDF methods

“…This approach overcomes the limitation of the implicit coupling with velocity by including appropriate models for this dependance. [2][3][4] In the PDF approach, the PDF transport equation needs to be solved along with the LES flow equations. For a N s -species system, the PDF equation spans N + 5 dimensions.…”

“…A fully Eulerian approach, termed the direct quadrature method of moments (DQMOM), was formulated to overcome this issue. 3,4,8,9 In this work, the DQMOM approach will be used to solve the PDF transport equation.…”